To achieve good performance of certain functions, living systems are
inherently nonequilibrium and dissipative. Recently, the relationship
between biochemical functions and nonequilibrium thermodynamics has
been an active area in statistical physics community [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}.
For instance, Lan \(et\)  \(al.\)  have revealed a powerful trade-off
relation between energy dissipation rate, adaption speed and the maximum
adaption accuracy underlying many sensory systems [3]}, [4]}.
Lang \(et\)  \(al.\)  have investigated the fundamental thermodynamic
constraints on statistical inference and learning of biochemical signaling
networks [6]}. Particularly, for biochemical
oscillations which are essential in regulating the timing of life
processes, such as the cell cycle, circadian clocks, and glycolysis,
both accuracy of the period and sensitivity to external cues can be
ensured by dissipative processes simultaneously [24]}, [25]}, [26]}, [27]}, [28]}, [29]}.
Therefore, it is important to measure the free energy dissipation
in biochemical oscillation systems that maintains the cyclic dynamics.
However, in actual experiments, how to infer the energy dissipation
is of great challenge [30]}, [31]}.
